The volumes containing significant elements of internal submicrocrystalline and nano structure of material are investigated by numerical methods of continuum and quantum mechanics. In proposed project, a critical review on the validity of different experimental and theoretical approaches to the mechanical properties of nanoscale structures and advanced nano reinforced composite structures will be presented. The number of mechanical properties (Young modules, Poisson ratio etc.) of single nanoclusters and the reinforced composites under different loadings will be compared and studied using molecular dynamics (MD), classical elastic shell theory and closed-form elasticity solution (EL), boundary elements method (BEM) and finite element method (FEM). The FEM-based technique and computer simulation will be presented for modeling of nanomaterials at different scales on example of carbon-based structures. Study of single-layered graphene atom and then graphene sheet is fundamental in nano-scale because fullerenes and carbon nano tubes are viewed as deformed graphite sheets. The purpose of the research is numerical FEM modeling of mesovolumes of such materials. For a realistic simulation of the stability behavior of carbon nanotubes, the nonlinear intramolecular inter-actions between neighboring atoms have to be taken into account. In order to reduce computational costs, it is necessary to develop suited homogenization techniques, so that shell elements can be applied. Heterogeneity of stressed state is typical for deformation of mesovolumes of a structurally inhomogeneous material. The work was done in collaboration with team members of Prof. Zhores Alferov, the Nobel Prize Laureate in Physics at the Ioffe Physic-Technical Institute in St. Petersburg, Russia.
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